Cremona's table of elliptic curves

8008 = 2³ · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 7+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	8008b	Isogeny class
Conductor	8008	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1408	Modular degree for the optimal curve
Δ	-23319296 = -1 · 28 · 72 · 11 · 132	Discriminant
Eigenvalues	2- -1 -3 7+ 11+ 13+  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,23,221]	[a1,a2,a3,a4,a6]
Generators	[-1:14:1] [7:26:1]	Generators of the group modulo torsion
j	5030912/91091	j-invariant
L	4.1471007170742	L(r)(E,1)/r!
Ω	1.5924051641887	Real period
R	0.3255374959164	Regulator
r	2	Rank of the group of rational points
S	0.99999999999988	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16016d1 64064h1 72072l1 56056r1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8008b1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-1	-3	+	+	+	0	0	-7	0	-7	-7	-4	-2	0	-10	-9	-12	-7	1	6	-8	6	-13	-11

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Quadratic twists for elliptic curve 8008b1

-4	8	-3	-7	-11	13
16016d1	64064h1	72072l1	56056r1	88088r1	104104l1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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